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The total charge in a volume with charge density \( \rho_v \) is obtained by

  • A.integrating the density over the volume
  • B.multiplying the density by the surface area of the volume
  • C.taking the divergence of the density throughout the volume
  • D.integrating the density over the bounding surface of the volume

Answer: A

Charge density is charge per unit volume, so the total follows from \( Q = \int_v \rho_v \, dv \) with the appropriate volume element for the coordinate system in use. For a uniform density the integral reduces to the density times the volume.

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